2.2 Congruences

Why cannot we cancel the \(2\)'s in the equation \(8\cdot 2 \equiv 3 \cdot 2 (\text{mod } 10)\) to \(8 \equiv 3 (\text{mod } 10)\)?

Exercise 1

  2 is a prime number 2 is even 2 has common factors with 10 10 is not a power of 2 We CAN cancel the 2 2 has common factors with 10 

If \(k\) and \(n\) are _____, then \(k\) has a multiplicative inverse in the equation \(a\cdot k \equiv b\cdot k (\text{mod } n)\).

Exercise 2

  collinear of different parity relatively prime invertible irreducible distinct relatively prime